Ronny Jordan joined a very exclusive club when he turned a jazz instrumental into a pop hit. Photograph: David Redfern/Redferns

The jazz guitarist Ronny Jordan, who has died aged 51, was a gifted self-taught performer of warmth, humility and spirituality, who became famous for crossing a thoroughly worldly hurdle – vaulted by Dave Brubeck and very few others – when he turned a jazz instrumental into a pop hit.

In 1992, Jordan's hip-hop and funk-influenced version of the Miles Davis theme So What became a cult dancefloor success, elevating the young guitarist from Harlesden, north London, into one of the key figures of the 1990s acid-jazz movement. Like his superstar fellow guitarist George Benson and other crossover artists such as George Duke, Donald Byrd and Roy Ayers, he was a populist who could irritate aficionados, but his sound was his own and not a formula. The contrast between the punchy funk rhythms of his backing bands and his own graceful and lightly struck guitar sound was the secret of his best music's mellow subtlety, and widespread popularity.

To some it was elegantly executed radio-play music with a jazzy gloss. But Jordan was genuinely devoted to the work of the great jazz guitarists of the swing and hard-bop eras – notably Charlie Christian, Django Reinhardt, Wes Montgomery and Grant Green – and in the right circumstances would pay his respects to them with joyfully breezy virtuosity. When he played at Ronnie Scott's club in 2004, his playing rippled with Montgomery's warm chording and sleek octave slides, snapped with a succinct bluesiness, and took off most ecstatically on Green's Sunday Mornin', the kind of holy-rolling gospel vehicle that had been second nature to Jordan from childhood.

The second of seven siblings, Jordan was born Robert Simpson, to Jamaican parents, in London. His father, Laurence, was a church deacon and his mother, Anzel, a dressmaker, was also involved with the church as a pastor. Ronny taught himself to play the ukulele at the age of four and the guitar at eight, performing for his father's church congregations. By 13 he was leading his own band.

He took a business degree and initially worked in a variety of non-musical jobs, but kept on listening – to jazz musicians, to guitarists from Jimi Hendrix and Eric Clapton to Chuck Berry and T Bone Walker, to soul and funk artists including Parliament/Funkadelic and Tower of Power, and to early hip-hop pioneers. That mix found its way into a self-made single, After Hours, which was rejected by record companies at first. But as the 1990s dawned, the climate for a new synthesis of jazz and pop was about to change.

By the beginning of the 1990s jazz-loving DJs such as Gilles Peterson and Paul Murphy had been introducing the most soulfully danceable tunes from jazz's hard-bop era to London clubbers, sowing the seeds of what would become "acid-jazz". Jordan's 1992 version of So What took off on the dancefloors, Island Records signed him for a debut album (The Antidote), and his role on the Gang Starr leader Guru's album Jazzmatazz Vol 1 quickly accelerated his fame. Jordan reached the UK top 30 in 1993 with the song No Time to Play, on which he hooked up with Guru and the vocalist Dee C Lee.

His 1995 remix album Bad Brothers was faulted by some as formulaically smooth jazz, but his live performances had become internationally popular. Blue Note signed him in 1999 after his move to New York, and the resulting album A Brighter Day (2000) was an altogether more substantial and focused mix of American, Latin and Asian music that reached the top 10 on Billboard's jazz chart and attracted a Grammy nomination.

Jordan won a Mobo award for best jazz act the same year and his song The Jackal was lip-synched by the actor Allison Janney in the role of CJ Cregg for the hit TV drama The West Wing. In 2001 the Gibson company made him its guitarist of the year. Jordan kept touring – notably, for London fans, playing a Jazz Cafe gig in 2010 in which he was joined by Benson himself.

In 2013 Jordan brought out a digital release of a new project, Straight-Up Street – a studio venture mainly featuring synth-guitars, with a little turntable and drum-programming assistance. His efforts to fund its expansion to a CD and a tour through investment from fans stalled, but the project confirmed his enduring belief that a restoration of jazz to pop music status was a dream worth pursuing.

Jordan is survived by his siblings, Rickey, Denise, Faye, Gaynor, Darren and Clive.